A Reconstruction of the Hippocratic Humoral Theory of Health.W.balzer-A.eleftheriadis

A Reconstruction of the Hippocratic Humoral Theory of HealthAuthor(s): W. Balzer and A. EleftheriadisSource: Journal for General Philosophy of Science / Zeitschrift für allgemeineWissenschaftstheorie, Vol. 22, No. 2 (1991), pp. 207-227Published by: SpringerStable URL: http://www.jstor.org/stable/25156549 .Accessed: 08/04/2011 11:37

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A RECONSTRUCTION OF THE HIPPOCRATIC HUMORAL

THEORY OF HEALTH

W. BALZER and A. ELEFTHERIADIS

SUMMARY. The model underlying the hippocratic humoral theory, as well as the corre

sponding part of hippocratic aetiology is reconstructed in precise, structuralist terms. Stress

is laid on the presentation of the model, historical and philological derivations are suppressed. The global net structure of humoral theory in which the different diseases are described as

specializations of the basic model is worked out, and the particular metatheoretical features

of 'therapeutical' theories, as contrasted to 'descriptive' theories, are exemplified and stated

in general.

Key words: medical theory, theoretical medicine, humoral pathology, axiomatization, struc

turalism, model theory.

INTRODUCTION

This paper presents a logical reconstruction of what may be called the theory of the four humores as laid down in the Corpus Hippocraticum, in parti cular in the work 'Nature of Man'.1 The paper emends and simplifies the

account given in (Eleftheriadis, 1991). It is intended to serve several purposes.

First, a consistent, and comprehensive account of this theory is given in axiomatic form. This cannot be achieved, of course, by mere abstraction

from the original hippocratic texts, nor by mere philological or historical

studies: gaps have to be filled, missing links to be introduced, inconsistencies to be eliminated. Reconstruction involves construction. We tried to stick

to the historical material as close as possible, concentrating on the Corpus

Hippocraticum2. However, in this paper we do not want to go into the

philological and historical 'derivations' of our model which would fill a

paper of its own. Rather, we concentrate on presenting the resulting model as well as some derived meta-theoretic features in a way as clear and precise as possible.

Second, we want to make clear that Hippocratic humoral theory exem

plifies all features which have been regarded essential to empirical theories

in general according to the general meta-theory now known under the label

of 'structuralist' approach to theories.3 On the one hand this shows that

medical theories, in fact, may be regarded as proper empirical theories.

On the other hand this yields a further successful application of the

structuralist meta-theory.

Thirdly, this work is intended as a contribution to the continuing discussion on the methodological status of medical theories.4 The example

Journal for General Philosophy of Science 22: 207-227, 1991.

? 1991 Kluwer Academic Publishers. Printed in the Netherlands.

208 W. BALZER AND A. ELEFTHERIADIS

studied exemplifies all the properties of empirical theories in general, that

is, hippocratic humoral theory has to be regarded as an empirical theory

proper. Moreover, in Sec. IV, an important distinction to the 'normal' form

of theories in the natural sciences is pointed out and exemplified.

I. THE BASIC PICTURE

According to 'The Nature of Man'5 four humores or cardinal fluids exist

in the human body whose state of 'mixture' (krasis), 'bulk' (plethos) and

'power' (dynamis) is decisive for health and disease.6'... he enjoys the most

perfect health when these elements are duly proportioned to one another

in respect of compounding, power and bulk, and when they are perfectly

mingled'.7 Thus a person's health depends on three characteristics of his

body's humoral state: first, it depends on the mixture of the humores; health can obtain only in case they are mixed. Second, 'qualitative intensity' of

the humores, and third, their quantities have to obtain in the 'right measure'.

This ideal mixture-balance humoral standard (eukrasia) is not the same

in every individual, it makes up the special nature of a person's body8, and the special humoral condition of his health. If this standard obtains we say that the state of the person is eukratic.

Now the person may be exposed to causes which destroy the optimally

proportioned humoral state, so that either one of the four humores increases or is in lack or becomes qualitatively more intense than the others, and

is isolated in some sense. The person then becomes sick.8 Therapy consists in finding out which of the humores have run out of their range of equilibrium

and in diminishing or increasing their quantities, qualities, or mixture so

that equilibrium is restored.

Of course, the notion of a chemical substance was not available at these

times (about 450 BC), so the humores represent a rough typification of

directly observable, qualitatively different liquids or 'juices' being present in the body, being produced by it, or leaving it. Not every kind of body

liquid is regarded as a different humor, this label is reserved for only four

of them: yellow bile, black bile, blood and phlegm. These four humores are intimately connected with the four elementary

qualities of the human body: warm, cold, moist and dry. Yellow bile is

warm and dry, black bile is cold and moist, blood is warm and moist,

phlegm is cold and moist. We say that each humor is the 'carrier' (cpopefc) of two qualitative intensities (dynamies).9 These qualities may be present in different dregees10, ad they vary with the quantities of their corresponding

humores.11

Concerning the different quantities and qualities of the humores numerical

representations seem natural from a modern standpoint. However, such a representation would conflict with the historical background. We have to be aware that the concept of a quality still was in its process of formation, the concept of a real valued function used today to represent qualitative

THE HIPPOCRATIC HUMORAL THEORY OF HEALTH 209

orderings did not exist. Furthermore, no strict ways of measuring the

qualities were known, and no attempts at measuring the quantities of the

humores were made. Consequently, the hippocratic formulations concerning mixture and equilibrium remain very qualitative. There is only 'more or

less' of some humor or of some quality - in accordance with what could

be observed. For these reasons we avoid numerical representation and stick

to a qualitative treatment of humores and qualities. This yields an apparent

complication of these notions in our reconstruction. From a logical point of view, however, our treatment is less complicated, and 'more basic'.

The basic models comprise two parts. First, there is a statical part which

attempts at clarifying the concept of a state of equilibrium or health. Sec

ond, the dynamical part provides a picture of how certain factors may

change the states of a pearson over time, and consequently how equilibrium

(health) may change into disequilibrium (illness), and how the latter may be treated.

II. PRIMITIVES AND POTENTIAL MODELS

The central notion of a humor we represent by a weak order, i.e. by a

structure < D, ^> consisting of a set D of abstract 'degrees' and a relation

^ on D which is transitive, reflexive, and connected. We introduce four

such orders, one for each humor. The four qualities we comprise into two

weak orders, one for warm-cold, and one for moist-dry. Though Hippocrates

always keeps the four qualities seperate, nothing gets lost by combining the two opposite qualities of each pair into one respective weak order.

We abbreviate the humores according to the following list:

(1) hx =

yellow bile, h2 = black bile, h3

= blood, hA

= phlegm,

and we denote the corresponding weak orders in the form <| | ht\ |,<,->, for i =

1, 2, 3, 4, so ht =

<11 ht \ | ,^,>. Index / in the following will always range over these four humores. Similarly, the two weak orders for the qualities are denoted by

(2) ql -

temperature, q2 = moisture

where each ql has the form ql =

<| | ̂| |,^'*>, and index i will always

range over 1,2 in the following. As usual, we define equivalence and strict

order in terms of ^ by: (a ? b iff a ^ b and b ̂ a) and (a < b iff (a < b

and not b ̂ a)). A person at each time has a distinct state comprising the four degrees

of its humores, the eight degrees of the qualities corresponding to these

humoral degrees (two for each humor), and one further item indicating whether the humores are in mixture or not. So each state s(t) at time t

is a 13-tuple

1y(/)=<Cz1,...,z4,z5,...,z8,Z9,...,z12,z13Z>


where zx,...,zA are degrees of the humores hu...,hA, z5,...,zs are degrees of

the quality q1, z9,...,zn degrees of quality q2, and z13 is one of the two

signs V (for separated) and '?1 s' (for not separated). Defining

St =

\W\\\ ^Hl<72ll4, SQ =

StxSw and

^ =

||Ail|x...x||A4||.

each such state is an element of the 'state space': SH x Sq

X {s, ?\s}. Elements of SH we will call humoral states, and elements of

Sq qualitative states.

Whereas the information that the humores are in mixture is expressed

by the symbol'?15', the notions of quantitative equilibrium of the humores

and of qualitative equilibrium of the corresponding qualities afford further

primitives. We use two sets

POSCS^ and BALCSg to contain exactly those tuples of degrees which are in quantitative, humoral

equilibrium (7roo6rrjTa) and are balanced with respect to their qualitative intensities, respectively. These two notions have a rather theoretical status.

The assignment of degrees of qualities to degrees of humores is captured

by two functions 0,: 11 h{\ |U...U| | hA\ \ -

\ \ql\ | and &w: 11 hx\ | U ... U 11 hA\ \ ""** 11 <72l I ?t(u)

= v means that the humoral degree u 'has' degree v of quality ql (e.g. a given degree of blood has a certain temperature), and 0w(w)

=

v means that the humoral degree u has degree v of quantity q2. Further

more, we employ a function core to assign qualitative states to humoral states. corQ can be explicitly defined with the help of 0t and 0W:

core (zl5...,z4) =

<0/ {zx),...,%t(zA), ^w{zx),...,^w{zA)>.

In addition to these notions central for the theoretical concept of

equilibrium, there are others concerning the description over time. First, of course, time itself is needed. We represent it by a linear order <T,< >, where T is supposed to be a finite, non-empty set (representing points of

time) and < C T x T is transitive, anti-reflexive and connected. If t* is

the maximal element of T with respect to <, then by T* we denote T\ {t*}, and for each t e T* we denote by t+\ the unique t' e T such that t <

/' and there are no /" e T such that t < t" < f. The function s(t) already mentioned then may be typified precisely by s:T ?

SHx SqX {s, ?1 s}. The 'observational' state of health of a person is described by a function:

g:T ?

{healthy,ill}. Finally, we use a set F of 'factors' and a function a

describing how these factors affect the different humores, their qualities, and the state of mixture. We write a(tf)=<h, a, q, b, c>, to be read as

'at /, factor / affects humor h in direction a, quality q in direction b, and mixture of humores in direction c. a, b, c range in the sets {+,-,0}, {+,-,0} and {s,0}, respectively where '+' and '-' indicate the directions express ed by 'greater' and 'smaller' in the natural reading of the orderings < D,

^ >, s indicates '/ is seperating', and '0' neutrality. Altogether we may


define, in structuralist format, the class Mp

of potential models as follows.

DI x is a potential model of hippocratic theory (x e MS) iff there

exist hl9 ..., h4, q\ q2 and T, H, Q, F, < ,s,g, POS, BAL, 0? %w and a such that x=<T, H, Q, F, <,s, g, POS, BAL, 0? %, a > and

(1) <T, < > is a finite, linear order

(2) H={hu...,hA] and each ht is a finite weak order

(3) Q={<l\ 42} and each ql is a finite, weak order

(4) s:T-+ SHxSQ x{s, ?i s}

(5) g.T- {healthy,111} (6) POS C SH (7) BAL C

SQ (8) 0,:||/*J|U...U||/*4||HI<71II (9) 0W:||/*J|U...U||/*4||HI<72II

(10) F is a non-empty set

(11) a:TxF-(Hx {+,-,0} x Q x {+,-,0} x {j,0})

We may suppose that all orderings are finite because the means of

differentiating the degrees in antiquity were very limited so that only few

degrees could be distinguished. Elements of T, H, Q, and F are interpreted

by points of time, humors, qualities and factors, respectively. Function s

describes the states of humores, qualities and mixture over time, while g

yields a direct description over time of whether the person is healthy or

not. Elements of POS and BAL may be called humoral states in quantitative

equilibrium, and states of qualities balanced in intensities, respectively. St and 0^ to each humoral degree assign its corresponding (degrees of the) qualities temperature and moisture, a describes which factors are effective at what time, and how they affect the humores and their qualities.

Each potential model comprises the concepts necessary to describe one per son, whether healthy or sick. Different persons being captured by different po tential models, there is no need to mention the person in the potential models.

III. THE MODELS

In order to state the axioms characterizing the models, some auxiliary definitions are helpful. We say that a function 3>:D ? D' mapping the sets from two structures <D, ^> and <D', ^'> on each other is order

preserving (respectively order reversing) iff, for all a, b e D: a ^ b iff <!>(#)

^'<l>(&) (resp. a ^ b iff $(b) ^'&(a)). Clearly, for all week orders <D, ^> and <D', ^> the following holds:

(3) if <b:D ? D' is order preserving (resp. order reversing) then the same holds with respect to < (as defined above). Moreover, for all a,b e D: not (a < b and b < a).


If z=<zlv..,z8> e Sq

we define a1(z)=<z1,...,z4> and o2 (z)=<z5,..., z8>. If z=<zlv.., z12, z13> e SHX SqX {s,?]s} then /}(z)=<z1,...,z4> and, for

k <: 13: nk{z)=zk. Finally, if, for i ̂ 4, </),, sg,> are weak orders, and

v=<vlv..,v4>, w=<wu...,w4> e Dx X ... X Z>4 then w is a one-sided deviation

of v iff (for all i ̂ 4: v, ^ t Wt and there is i ̂ 4 such that vz < f w,-) or (for all / ̂ 4: wf ̂ t vz and there is / ̂ 4 such that wt < { vt).

Now the axioms for the basic models of hippocratic theory may be

formulated. The central axiom is concerned with the mixture-balance

condition of health as described above, and says that a state s(t) of a healthy person is such that it's 'humoral part' /? (s(t)) is a state of quantitative (noooTriTa) equilibrium of the humores (i.e. element of POS), it's 'qualitative

part' is in qualitative balance (i.e. an element of BAL), and it's component

describing mixture indicates that the humores indeed are mixed (i.e. in state

?\s). This is formalized in D2-1 below. We do not require the reverse

direction expressing that if a state s(i) satisfies the mixture-balance condition, the person is healthy at t. The basic reason is that this would make the

'observational' representation of health, g, explicitly definable and thus in a certain sense redundant. Our weaker version allows for observed illness even if all theoretical conditions for health are satisfied.

Axiom D2-2 regulates the 'directions' in which the qualities vary when the humores vary. Hippocrates does not combine 'warm' and 'cold', nor

'dry' and 'wet' into a single scale, respectively, as we do. He uses the following

assignement12

yellow bile warm dry black bile cold dry blood warm wet

phlegm cold wet

Any humor's qualities are supposed to vary in degree with variation of

that humor. Thus increase of blood, for instance, leads to increase of warmth and moisture, and conversely.13 Note that we deal with weak orders so

that 'increase' includes 'no change'. By combining the qualities 'warm' and

'cold' to one scale 'temperature' we have to be careful about directions

of qualitative change. If phlegm, for instance, increases then according to

the above list coldness also increases, that is: temperature decreases. So

0, is order reversing when restricted to the degrees in ||A4||. Proceeding in the same way for all the four humores we obtain the eight requirements stated in D2-2.

D2-3 below imposes a strong condition on the notions of qualitative balance and of quantitative equilibrium of humors. It says that two

'qualitative' states such that one is a one-sided deviation of the other cannot

both be balanced, and the same for humoral states.

Axiom D2-4, finally, captures the dynamical part of the model. It draws a connection between the affect-function a and corresponding changes of

humoral or quality degrees. For example, 2-4-b.3 states that if a assignes


a pair <ql,+> at time t to factor / where ql is a quality of humor ht, then

the degree of ql corresponding to ht will increase, i.e. will be greater at

time f+1. The j4+/'s projection just picks out the right component of the states s(t), s(t+l), namely the component describing the degree of quality

qi of hj. For i=2 and j=2, for example, h2 is black bile, ql moisture, and

according to the above definition of core qrs degree has to occur in position number 10 (= /4+/) of a state s(t). 4-a states that a factor causing separation leads to a humoral state which is not mixed at the following instant, and

4-c says that 'neutral' factors do not yield any change of the corresponding

degrees.

D2 x is a model ofhippocratic theory (xeM) iff there exist hx,...,hA,qv,q2 and T,H,Q,F, <,s,g,?OS,BAL,@t,@w such that x =<T,H,Q,F,

<s,g,?OS,BAL,?t,%> (0) xeMp (1) for all t e T: if g(t)=healthy then fi(s(t)) e POS, corQ (p(s(t)))

e BAL and ttu (s(t)) = ?\s

(2) 0/| | hx\ | + 0/| | h3\ |, 0^/11 h3\ |, 0W/| | h4\ | are order preserving and

(3.1) for k=\, 2 and for all z,zf e Sq.

if ok{z) is a one-sided deviation of ok(z!) then not (z e BAL and z' e BAL)

(3.2) for all z,z' e SH, if z is a one-sided deviation of z' then not

(z e POS and z' e POS)

(4) for all te T*, i ̂ 4 andy ^ 2:

(a) for all r e F and a,b: if a(tf)= <hi,a,qJ,b,s> then not /?(,$(*+1)) ePOS

(b.l) (there are/,Z?,c such that a(tf)= <ht, +, ^, Z?, c>) iff ttj (s(t))

</7r/(s(t+l)) (b.2) (there zrtfb,c such that a(f,t)

= <hi9 -, ^, b,c>) iff tt,- W/+1))

(b.3) (there are f,a,c such that a(tf) =

<ht, a, qi, +, c>) iff nj4+i

(s(t))<J7rJ4+i(s(t)) (b.4) (there are f,a,c such that a(tf)

= <ht, a, qi, -, c>) iff

7Tj4+i

(s(t+l))<i7rJ4+i(s(t)) (c.l) for all/,*,c: a(tf)

= <ht, 0, qi, b,c> iff nt (s(t))

? tt{ (s(t+\))

(c.2) for all f,a,c: a(tf) =

<ht, a, qi, 0, c> iff tt^,- (s(t)) ^7r-4+/ W/+1))

IV. DISEASE

The models introduced do not characterize disease by themselves, they just

provide a conceptual model in which health as well as disease may be

described, together with the development of disease. According to the

structuralist meta-theory, any empirical theory (theory-element) consists of at least classes M M and a set of intended applications, i.e. a set of non-theoretical descriptions of those real systems to which one intends to


apply the theory. In medical theories this minimal scheme needs emendation.

Besides the models which describe the 'normal' or 'healthy' cases or are

neutral with respect to health and disease there is definite need for the

introduction of another set of structures, which we call S in the following, the elements of which characterize disease. The argument for introducing

S is this. On the one hand, it is clear that the intended applications for

a medical theory are given by cases of sick persons. Medical theories are

intended to explain sickness and thus to guide therapy. On the other hand, we cannot simply take as models of a medical theory only those structures

which characterize disease. For if we did so, we would loose any standard

of health. In general we would risk to 'systematize sickness' without caring about how to cure it. In order to satisfy both these requirements: to keep a standard of health, and to characterize disease, there seems only one

way. We have to emend the general structuralist picture, and add another

component, S, to those making up a medical theory. Thus the basic theory-element of hippocratic theory takes the form

<Mp,M, S,I>

where Mp

and M are as before, / is a set of descriptions of intended cases14

in the vocabulary given by the potential models, and S C M is a class

of structures characterizing sickness.

Sickness may be characteried by specializing the general models in M.

Further assumptions are added separating those models describing sick

persons from the others. These assumptions may be stated at the obser

vational level of g, or alternatively on the theoretical level involving reference

to mixture and balance. Observationally, a person captured by some model

is sick at time t just when g(t) = ill in that model. A corresponding theoretical

characterization is this.

D3 (a) x is a model of a person sick at t iff there exist hx,...,q2, T,...,a such that

(1) x=<T,...,a> and teT

(2) x e M

(3) not: s(t) e POS X BAL X { -n j} (b) x is a model of a sick person (x e S) iff there existx / such

that x is a model of a person sick at t

The idea here is, of course, that the set POS X BAL X {?\s] characterizes

exactly those states in which the person is healthy. Instead of the existential

condition for t in (b) we might also work with a universal quantification. In the light of the previous discussion we note the importance of condition

D3-a-2. If this were omitted we had no standard for justifying condition

(3) to express illness. By virtue of D2-1 we obtain

Tl If x=<T,...,g,...> is a model of a person sick at t then g(t)=il\

The reverse of Tl does not hold in general. It holds iff D2-1 is replaced

by an equivalence.


V. THE THEORY-NET

If this were all about disease then the hippocratic theory would not have

gained much influence. The crucial point which makes it interesting, and

in which it exemplifies the situation typical for mature theories in the natural

sciences, is that the theory-element described up to now forms the basis

for many interesting specializations, each specialization being connected

with a special kind of disease. The general picture of mature empirical theories which emerged from structuralist studies15 is that of a theory net,

consisting of one basic theory-element (like <M , M, S, /> described above) and many specializations of that basic element. This is why we used the

term 'theory-element' above.

A specialization of the basic theory-element described above is obtained

in three steps. First, new terms are added to those used to define the potential

models, second, new requirements are added to those defining the models.

Third, it is necessary to narrow down the set I of intended applications for the new assumptions made in step two will not hold in all applications of the basic theory-element. The classes of potential models and models

are left unchanged. So a specialization of <M M, S, I> is an entity <Mp, M, S*, I* > where S* C S and 7* C I.16

Abstractly, we may introduce special ways of disease corresponding to

possibilities of deviations of a person's state s(t) from a virtual state s*(t) of health. Considering a state s(t) which deviates from a state of health

just in one component zt, i < 13, and which is a state of sickness (i.e. not in POS X BAL x {?\s} we may say that a person in state s(t) yields a model for a disease due to, or 'caused by', the humor or quality indi

cated by index i. If s(t)=<zu...,zn> and k < 13 let us write s(t) [zk/zk*] to denote the result of replacing tk in s(t) by zk*. In the same way, we

may further specify whether it is lack or abundance of zt that causes the

disease.

D4 Letx=<T,...,a>eM.

(a) For / < 4, x is a mode I for a disease caused by lack of (abundance

of) ht iff there is some t e T and some z^zi such that s(f) e/POS x BAL x {?is}, s(t) [Zj/z*]* POS x BAL x {?\s} and zi<izi*(zi*<izi)

(b) For / < 4 and j < 2, x is a model for a disease caused by

lack of (abundance of) qi with respect to ht if there is some

t e T and z^zt such that s(t) t POS X BAL X {?\s}, s(t)

[zj4+i /zj4+i\ e POS X BAL x {-.s}, and

zJ4+i <j zj4+i

(Z*j4+i<JZj4+i) (c) For / < 4, x is a model for a disease caused by humor ht iff

x is a model for a disease caused by lack or abundance of ht (d) For / < 4 and j

< 2, x is a model for a disease caused by

qi with respect to ht iff x is a model for a disease caused

by lack or abundance of q- with respect to ht


(e) x is a model for a disease caused by separation iff there is t eJsuch that oX3(s(t))=s

In D4, the states j(Otz/^/*] are possible states of health which are different from the actual states given by s(t). As the actual states deviate from these 'standards of health' they represent states of illness. We do not require that x in D4 be a model of a sick person. This can be proved.

T2 All special models defined in D4 are models of sick persons.

The proofs of the theorems are given in the appendix. Each clause in D4

defines several specializations Sr in the formal sense of subsets of S. By taking intersections we obtain further specializations characterizing diseases in which several humores or qualities are out of equilibrium simultaneously. In this way we obtain specializations which ultimately cover the cases

reported in the Corpus Hippocraticum. As a concrete example, consider

epilepsy. According to Hippocrates this disease is caused by some affection

of phlegm and blood in which

...the phlegm flows cold into the blood which is warm, ... If the flow be copious and thick, death is immediate, for it masters the blood by its coldness and congeals it. If the flow

be less, at the first it is master, having cut off respiration; but in course of time, when it

is dispersed throughout the veins and mixed with the copious, warm blood, if in this way it be mastered, the veins admit the air and intelligence returns.17

In the first case, basically, blood here gets too cold by the coldness of

phlegm which flows in. It is easy to define a specialization Sp of S in

which, at some t, the person's phlegm and blood are too cold. We even

may go further and introduce a specialization S pi by introducing further

concepts and, with their help, stating the symptoms of epilepsy. In this

way we arrive at a rather specific theoretical (and observational) description of the disease.

Similarly, we may proceed for many other diseases found in the Corpus

Hippocraticum, and we obtain a whole net of specializations, each of which

given by a subclass of S. Writing Sj for diseases caused by humor hif and

St: for diseases caused by quality cfl of humor hf, and St+, Sf etc. for diseases

caused by abundance or lack of ht, respectively, we obtain various knots

in the theory-net depicted in Figure 1 on the next page. A second kind of specialization is concerned with prognosis. This

specialization already is a bit involved so that we can sketch it only very

briefly. It refers to four new concepts: 'critical days', 'maturation', 'secretion'

and 'improvement (of the state of health)'. Critical days in a process of

disease are those which in some sense are crucial for the further course

of the disease. For fevers, for instance, the critical days are: the 7th, 9th,

11th, 14th, 17th and 20th day.18 Specific events on these days indicate whether

the patient will get better or worse. In the case of 'pains of the lungs and

ribs', for instance, 'sputum should be quickly and easily brought up, and

the yellow should appear thoroughly compounded with the sputum; for


_^ M(HP) ^^^

diseases of the 4 prognosis

humores// ^"^^ S \

y^ I \ ^*\. improvement \

Sf. yellow S2: black S3: blood S4: phlegm^

\

bile .bile I \ \ VV \

\\ \ \ Ny. \ ^v deterioration

\ \ ardent \ N. \ >s^ \ \fever \ N. \ pneumonia

S.+: jaundice \ \ \ >v \

phrenitis \ inflammation NA

continued | \ blood/phlegm fever tumor \ / \

quartan / \ fever / \

erisypelas sacred disease

Fig. 1

if longer after the beginning of the pain yellow sputum should be coughed

up, or reddish-yellow, or causing much coughing, or not thoroughly

compounded, it is a rather bad sign'.19 'Especially should the empyema

begin from sputum of this character, when the disease has reached the

seventh day, the patient may be expected to die in the fourteenth day unless

some good symptoms happen to him'.20 Maturation and secretion mainly refer to the case where disease is caused by abundance of a humor h. If

h maturates or is secreted on a critical day, an improvement of the patient's state will follow. Otherwise, things will get worse.

In order to deal with prognosis adequately, some way of blurring is

needed. We may introduce a probability space of the set of possible states

to this end, and thus finally obtain various specializations PROGj capturing various different ways of secretion, and in particular the two main cases

of 'improvement' and 'deterioration'. Adding them to the net of diseases we obtain some picture like that in Figure 1.

VI. THE MECHANISM OF DISEASE

In addition to providing a basis for a theory-net the models introduced

contain a precise picture of how diseases may originate, and be cured.


Roughly, sickness occurs whenever, at some time /, some factor / affects the person such that the effect of / is not counterbalanced by any other factor at t. So / causes some humores or their qualities to change while the others stay as they are. the result is some deviation from equilibrium and balance, and disease comes up.

In a first step we define the notion of supplementarity of two factors

(D5-a below) by their acting 'in the same direction'. By a cause of a disease we understand a set of factors all of which are supplementary. By requiring that such a set covers all the factors effective at some instant t we are

sure that no counterbalancing factors are present (D5-c).

D5 Letx=<T,...,a>eMp,

t e T.

(a) Let// e F, i,k < 4 and j,r < 2.

/and/ are supplementary iff, for all a,b,c,a',b\c': if a(tf)=<ht,a,qi,b,c> and a(tf)=<hk,a'9qr,b'9cJ> then

(1) if i=k then a-a' and c=c'

(2) if J=r then b=b'

(b) Ft, the set of factors effective at t in x, is defined by

Ft= {feF/ there are h,q,a,b,c such that a(tj) =

<h,a,q,b,c> and (aÔ or bÔ or cÔ)}

(c) Ft is a cause of disease in x iff

(1) Ft is the set of factors effective at tin x

(2) Ft is not empty

(3) for all// 6 Ft:f and/ are supplementary

We now can prove that in models of the hippocratic theory causes of

disease, in fact, lead to disease. In this sense, the theory may be said to

explain the origin of disease. Theorem 3 states this on an abstract level.

Specializing this account to various combinations of particular factors

leading to particular diseases, we obtain another theory-net of specializations

covering the field of anamnesis.

T3 Let x=<T9...9a> e M and t e T*. If #(/)=healthy and Ft is a

cause of disease in x then x is a model of a person sick at f+1.

In particular, g(t+\)=\\\.

VII. THEORETICAL TERMS

Most theories, at least the more comprehensive ones, allow for a classification

of their terms into theoretical and non-theoretical terms. Our idea of a

theoretical terms in theory T is that T should offer at least some ways for determining that term. Otherwise, the term is T^non-theoretical. This

distinction can be formalized21 but application to the present example will

be in informal terms. A T^non-theoretical term has to be determined 'outside'

of T, i.e. before Tis applied. If other theories are used in order to determine a T^non-theoretical term, then this term may be said to be presupposed

by T. Our idea of theoreticity therefore is closely linked with the way theories


are interrelated with each other in a hierarchical way. We will consider

only the relational terms here, those terms referring to the basic sets of

objects usually turning out as non-theoretical.

The relation of precedence in time (<) clearly is non-theoretical. Hippo cratic theory does not contribute to establish any means to determine which

instants are later than others. The same is true for the relations of compa risons (^)between degrees of humores and qualities. They also have to

be determined before the present theory is applied - either by qualitative

means like direct human sensation, or by some primitive devices of

measurement. This also holds for function s. The states in which the person is at various times are given by different degrees (of humores, qualities, and 'mixture'), and these degrees have to be determined beforehand. The

affect-function a also is non-theoretical. In order to find out which humor

is affected by some factor (and in what direction) we do not use Hippocratic

theory. Rather, we use observation and perhaps reasoning involving other, scientific or everyday, 'theories'. From what we said about our interpretation of g, g also is non-theoretical. The values of g are observed without recourse

to Hippocratic theory. Finally, it seems that the functions 0r and 0^ are

non-theoretical. In order to determine the degree of a quality present in a given degree of a humor we may resort to direct qualitative sensation.

The remaining terms are those used to characterize health: POS, BAL,

{s, ?\s} which are theoretical. In order to see that they are theoretical we must ask whether they can be determined without recourse to Hippocratic

theory. Now POS, BAL and {s, ?\s} are used to define states of health, i.e. elements of POS x BAL x { ?\s }. In order to find out whether some

state s(t) is in that set we have to use this definition, of course, and thus to refer to the theory. More locally: in order to find out whether a humoral state is in quantitative equilibrium (i.e. in POS) we have to see whether the theoretical assumptions put forward in D2 are satisfied, for these are

the only criteria we have for POS. One step in checking whether a humoral state is in equilibrium always will be to see whether g(/)=healthy, and by

means of D2-1 accept the assumption of equilibrium if no other facts point to the contrary. This step clearly involves reference to the theory. So no

theory independent method of determining POS seems to exist, and POS to be ^theoretical. This does not mean, of course that checking whether a state is in POS or not amounts to nothing else than the step just described. A typical means of determination is comparison among different persons.

Equilibrium of one person's humores is inferred from their being similar

to those in other persons which all were healthy. But this detour leads to the same kind of situation for the 'other' persons: at some point there are no others, and we are thrown back to the theoretical model.

The same holds for BAL. In order to see whether a qualitative state

is balanced (i.e. in BAL) we have to check, among other things, whether

the person is healthy in terms of g and to use D2-1 to infer that balance is acceptable in this case. Even in case of the set {s, ?\s] we come into


that situation. For in order to see whether a state is mixed or not we

cannot simply refer to the observed facts, at least in 'initial' cases where

there are no standards of comparison with other cases. Even in the presence of dramatic observational evidence with respect to mixture we have to check

whether the person is ill in terms of g, and then reason by means of D2

1, as before.

VIII. INTENDED APPLICATIONS

Any empirical theory is applied to real systems which 'anchor' the theory in experience. Those systems are difficult to characterize precisely. Usually,

they are given by 'paradigms'plus 'autodetermination'. In the development of the theory over time, first some real systems are pointed out ostensively and called 'paradigmatic' intended systems iff they yield models, that is, iff the theory can be successfully applied to them. The set of all descriptions of intended systems is called the set / of intended applications of the theory

(to which we referred already). All the concrete cases described in the Corpus

Hippocraticum may be regarded as paradigmatic, and all cases of sick persons

sufficiently similar to these yield intended applications.

According to the structuralist scheme intended applications are supposed to have the structure of partial potential models. Partial potential models

can be introduced in two ways, a more liberal, and a more narrow one.

According to the liberal version, a partial potential model is just any substructure of a potential model.22 A more restricted version in addition

cuts off all theoretical terms from those structures. We use M to denote

the class of all partial potential models in the more liberal sense.

Here are two examples.

Meton was seized with fever and painful heaviness of the loins. Second day. After a fairly

copious draught of water had his bowels well moved. Third day. Heaviness in the head;

stools thin, bilious, rather red. Fourth day. General exacerbation; slight epistaxis twice from

the right nostril. An uncomfortable night; stools as on the third day; urine rather black',

had a rather black cloud floating in it, spread out, which did not settle. Fifth day. Violent

epistaxis of unmixed blood from the left nostril; sweat; crisis. After the crisis sleeplessness;

wandering; urine thin and rather black. His head was bathed; sleep; reason restored. The

patient suffered no relapse, but after the crisis bled several times from the nose.23

Disequilibrium is indicated by the occurrence of humores: bilious stools

(indicating yellow bile), epistaxis, black urine, unmixed blood; and by some

qualitites being out of their usual range: fever, sweat.

Philiscus lived by the wall. He took to his bed with acute fever on the first day and sweating;

night uncomfortable. Second day. General exacerbation, later a small clyster moved the bowels

well. A restful night. Third day. Early and until mid-day he appeared to have lost the fever;

but towards evening acute fever with sweating; thirst; dry tongue; black urine. An uncomfortable

night; completely out of his mind. Fourth day. All symtoms exacerbated; black urine; a more

comfortable night, and urine of a better colour. Fifth day. About mid-day slight expistaxis of unmixed blood. Urine varied, with scattered, round particles suspended in it, resembling

semen; they did not settle. On the application of a suppository the patient passed, with flatulence,

scanty excreta. A distressing night, snatches of sleep, irrational talk; extremities everywhere


cold, and would not get warm again; black urine; snatches of sleep towards dawn; speechless; cold sweat; extremities livid. About mid-day on the sixth day the patient died24 (italics ours).

Again, the italicized expressions indicate the humores and qualities which are out of balance and equilibrium.

Descriptions like these may be formatted in the vocabulary of Sec. II.

Essentially, they contain data about time, g9 s9 and a, sometimes also about

the state of mixture. So we obtain a partial potential model, whether in

the wide or more narrow sense. Proceeding like this for all other cases

we obtain the set of all paradigm intended applications.

IX. CONSTRAINTS

Constraints capture relations among different models of a theory. Such

relations usually express features of stability of nature without which the

theory simply would not work. In hippocratic theory there are at least two

constraints.25

The first may be expressed by the slogan 'similar cause, similar effect'. In our vocabulary this may be made precise by reference to the affect

function a. If two potential models x, y represent two persons which at two instants t (in x) and /' (in y) are in the same state then a factor /

will affect both persons in the same way. In order to express this in precise terms, let us write, for potential models x, y: T*, V, sx9 ̂ etc. to denote

the components of x and y respectively. The constraint then may be

formulated as in D6-a below. Note that if the two states sx(t) and sy(t)

in x and y are the same then some of the humoral and quality degrees in x and y also must be identical. We also note that this constraint in

Hippocrates is used to characterize epidemics as diseases caused at the same

time or period by the same or similar factors in many persons. This points to a second constraint which is still more fundamental than

the first. Roughly, it says that the sets of degrees of humores and of qualities are (approximately) the same for all persons. In a very strict formulation

(D6-b below) this means that all these sets are identical in any two potential models. A similar constraint may be contemplated for the set of labels

{s9 ?\s} indicating separation, but this set is already identical in all potential models qua syntax.

D6 LctXQMp. (a) X satisfies the constraint for a (X e Ca) iff for all x9y e

X, all // and all/: if sx (t)=sy (/') then ax(t,f)=ay (t',f) (b) X satisfies the constraint for degrees (X e CJ) iff

for all x9y e X9 all / ̂ 4 and j ^ 2:

||Af|| =||^|| and 11 (90*11=11(^11 Of course, in the real world sets X satisfy these constraints only

approximately. Due to the individual differences of body and surrounding, the same factor (if we could identify it) will affect two persons in slightly


different ways. However, from the standpoint of hippocratic theory the humores and their qualities provide a complete description of a person's state. If this were so, then strict identity of states would not leave room

for any other relevant differences of the two persons - relevant with respect

to a - and D6-a would hold strictly indeed. This shows that the approxi mation necessary to make the constraints 'true' is 'proportional' to the

degree of completeness with which states s(i) describe a person. In case

of the constraint for degrees, one might say that different persons' being different even quantitatively, the humoral and quality degrees cannot be

the same for them. However, this constraint may also be read as an analytic statement about the notions of humor and quality. We simply choose one

maximal set of degrees for each humor and each quality such that the degrees of all persons are contained in that set. This set is entirely unproblematic, and satisfies Ca in a trivial way.

Further constraints are used in connection with the various specializations which capture different diseases. In many such specializations, some special constraint is at work. A factor/causing some particular diseases in one model

x, for instance, will cause the same disease (approximately) in other models.

It has to be emphasized that constraints play a major role in the

appplication of the theory. They allow to reason from one case (or from a set of similar cases) to another, new one. If symptoms (state) xyz are

the same for person p and all persons from a set Q, and if all persons in Q got disease XYZ in the past when exposed to factor j, then we will

infer that/? also will get this disease when exposed to factor/. This is just a verbal reformulation of D6-a. Without this constraint

(whether assumed or 'true') no medical theory would have developed. The same is true for Cd, but on a more basic level. If the degrees of humores

and qualities were not roughly the same for different persons, we could not compare them, and our knowledge had to be assembled anew in each case (with poor results of course).

X. EMPIRICAL CLAIMS

The distinction between theoretical and non-theoretical terms has some rele

vance in the context of applying the theory, in order to test whether it is

true. If we want to see whether some concrete cases, in fact, yield models

of sick persons we have to determine the sets, functions and relations

introduced in Section II. But if we use the theory in order to do so - which

is very likely in the case of theoretical terms, and impossible for non-theo

retical we already use (and in this sense: presuppose) it. In the context of

an empirical test of the theory it therefore is recommendable to determine

only values of non-theoretical functions. In order to check whether the axioms are true in a given system it then is sufficient to check whether the values

actually determined are compatible with the theoretical picture, that is, whether there exist theoretical augmentations POS, BAL, and {s, ?is} which


can be added to the observed data such that the axioms are satisfied.

By assuming that all intended applications yield such partial potential models, i.e.

IQMpp, the empirical claim associated with the theory-element

<Mp, M, S, T> may be formulated like this:

(4) for all y e I there exists some x e S such that x is an extension

of y

In one concrete case this means that the data which are known about a person (and which can be expressed in non-theoretical terms) fit into a model of the theory in which, for some suitable sets POS, BAL and

{s, s} all axioms are satisfied. In other words: for given (empirically

determined) functions <, s,g,<dt,?w and a there exists sets POS, BAL and

{s, ?\s} such that all these entities together (and together with the sets

T,H> Q,F) form a model of a sick person. Note that (4) refers to S rather

than to M. If S were replaced by M then (4) would not contribute to our

understanding that the persons considered are sick.

Adding the constraint the claim (4) may be considerably strengthened. Let us write C=Ca D Cd, and add C to the theory-element introduced before which yields an extended theory-element

(5) T=<Mp,M9S9C9I>

where Mp9

M and S are as before, C C Po(Mp)

and I C Mpp. Mpp

needs not to be mentioned in (5) because it is explicitly defined. The claim (4) then may be replaced by a claim for whole combinations (i.e. sets) of intended

systems. All intended applications have to satisfy (4) above, but in addition the extensions used in order to make (4) true have to satisfy the two

constraints. We thus arrive at the following definition.

D7 The empirical claim of the hippocratic theory-element <M M9 S9 C, I> is that there exists some X C M such that

(1) XQS (2) each y el has some extension in X

(3) XeC

In words: there exists a set X of extensions of the intended applications such that all these extensions are models and the set of them satisfies the

constraints.25

Of course, a realistic version of such a claim has to be blurred.26

APPENDIX

Proof of T2: Let s(t)=<z,,...,zl3> ^POS x BAL x {?i*}, k < 13 and zk* such that s(t) [zk/zk*] e POS x BAL x {s}. If A:=13 then zl3*zl3*= ?is, so zl3=s, and x is a model of a sick person. If 5 < k < 8 then <z5,...,z8> is a one-sided deviation of < z5,...,z8 >

[zk/zk*], and so, by D2-3, < z12,...,z12>


not in BAL. So s(t) e/POS X BAL X {?\s}. The same result we obtain

for 9 < k < 12. If k < 4, then <zlv..,z4> is a one-sided deviation of

<zlv..,z4> [zk/zk*] and from D2-3 we obtain that <zlv..,z4> is not in

POS# Proof of T3: Let x be given, f e T, g(0=healthy, and Ft be a cause of

disease. Let s(t)=<zx,...,zX2> and ^(/+l)=<z/1,...,z,12>.

From D5-b-l and D5-a we obtain

(1) there are a,b,c,ij and/e Ft such that a{tf)-<hi,a,qfb,c> and

not a=b=c=0

Case T. cÔ, i.e. c=s.

By M-5a, j3(.y(f+l)) j POS, so by M-l, g(t+\)=ill.

Case 2: aÔ, Subcase 2.1: a=+.

FromM-5-b.l:(2)z/</z'/.

Subcase 2.1.1: i= l,j=\. From (2) and M-2: (3) z5 <l z/5. Now let k e {6,7,8}.

Suppose zfk <l zk. Since k has the form 1 i+l, we obtain from M-5-b.4:

there are d,e and/ such that a(tf)=<hx,d,ql,-,e>, from which, by D5,

/ e Ft. So/and/ e Ft. From D5-b-3 and D4, together with (1) andy=l, it follows that b=-. So (1) reads a(tfl)=<hx,+,ql,-,c>, from which, by M

5-b.4 we obtain z/5<1 z5, which together with (3) in Section III and (3)

yields a contradiction. So the assumption is false, and therefore (4) zk<1 z*k. From (3), (4) and D2-e we obtain (5) < z'5,...,z,8 > is a one sided deviation

of <z5,...,z8>. From the general assumptions it follows that

<z5,...,z12>=cor(<z1,...,z4>) e BAL. This, by (5) and M-4 implies that

<zfx,...,zfX2> ? BAL. Since this is just cor(/$(s(t+1))), it follows from M

1 that #(/+l) = ill.

Subcase 2.1.2: i=l,j=2.

The proof goes as in Subcase 2.1.1 with '9' instead of '5', {6,7,8}, and

'^'instead of<^1',

The Subcases /=2,3,4 are proved similarly.

Subcase 2.2: a=-.

Subcase 2.2.1: a=l,j=\.

By M-5-b.2, (6) z,x <x zx. From this and M-2, (7) z/5 <l z5. Now let k e {6,7,8} and suppose that zk <1 fk. From M-5-b.3 we obtain

that for some d,ef, and hx, a(tf)=<hl,d,q1,+,e>, and so, by D4 and D5, b=+. But then (1) and M-5-b.3 yield z5<2 z/5, in contradiction to (7). So

zfk ^ z!k, and therefore <z'5,...,z/8> a one sided deviation of <z5,...,z8>.

As before, thies yields #(H-l)=ill.


The Subcases i=l, j-2, and similarly for /=2,3,4 are treated in the same

way.

Case 3: bÔ. Subcase 3.1: b=+.

Subcase 3.1.1: i= l,j=l.

By M-5-b.3: (8) z5 <l z*5. Let k e {6,7,8} and suppose z!k <{ zk. From M-5-b.4 this yields, for some d,ef,l, a(tf)=<hl9d9ql9-9e>. Since

// are supplementary, b=-9 so by (1) and M-5-b.4 z'5 <l z5, in contradiction

to (8). As before, we conclude that g(t+\)=i\\.

The cases y=2, and /=2,3,4 are treated in the same way.#

NOTES

) The Corpus is available in different editions: (Littre, 1962) and (Hippocrates, 1923). There

is no unanimity among historians whether the Corpus reveals one underlying common 'core'

or picture. We do not want to take side in this issue here which for our purposes we solve

by concentrating on those parts of the text providing a consistent picture. In particular, the

'humoral' part of our basic model comprises the ideas stated in 'The Nature of Man' and

'Ancient Medicine', the 'dynamical' part is based on 'Airs,Waters,Places', and the examples

(intended applications) are drawn from 'Epidemics V and 'Epidemics IIP. A survey of the

works in the Corpus dealing with, or containing part of, the humoral model is found in (Schoner,

1964). The importance of humoral theory for hippocratic medicine is described in (Temkin,

1928). 2) In particular on 'Prognostic', 'The Sacred Disease', 'Nature of Man' (ascribed to Polybos, son in law of Hippocrates), 'Epidemics I and IIP, 'Airs, Waters, Places', and 'Ancient Medicine'.

Morse about historical sources is found in (Sarton, 1970), pp. 348-84, (Schoner, 1964), (Temkin,

1928) and (Schumacher, 1963). The reader interested in more detailed links to the historical

sources is referred to (Eleftheriadis, 1991).

3) See (Balzer, et al., 1987) for a survey.

4) Compare (Fleck, 1980), (Kliemt, 1986), (Sadegh-Zadeh, 1980), (Westmeyer, 1972) and

(Wieland, 1975) for major contributions to this discussion.

5) This work is the only one in the Corpus discussing the humoral theory in a systematic

way, compare (Sarton, 1970), p. 368.

6) (Littre, 1962), Vol. 6, Chap. IV, p. 38.

7) (Hippocrates, 1923), Vol. 4, (repr. 1959, transl. by Jones), Ch. IV, p. 11.

8) '...for both constitutions and ages differ greatly' (Hippocrates, 1923), Vol. 3 (repr. 1959, transl. by Withington), Ch. VII, p. 113. (Littre, 1962), Vol. 3, Ch. VII, p. 440.

9) We use the term 'quality' instead of the hippocratic word 'dynamis' for a direct translation

would load it too much with physical connotations. It is characteristic that the hippocratics used the word VAÂo-?' to speak about 'quantity'

- to express the 'how much' of the humores

-, and the word 'Svvaijus' for 'quality' (^0167779), - to denote the 'how strong, intensive'

of them.

10) Today one would say 'quantities' instead of 'degrees', but this is likely to lead to confusing

expressions like 'the quantity of a quality'. We therefore systematically speak of 'degrees' of the four qualities.

n) (Littre, 1962), Vol. 6, Chap. VII. See also (Schoner, 1964), p. 20.

12) (Littre, 1962), Vol. 6, Ch. VII, p. 46, and (Schoner, 1964), p. 20.

13) (Hippocrates, 1923), Vol. 4, (repr. 1959, transl. by Jones), Ch. XII, p. 20.

M) More on the structure of members of I will be said in Section VIII.


15) Compare (Balzer et al, 1987), Chap. IV.

16) This definition is perfectly general, i.e. it takes the same form in the context of other

theories. In order to achieve that S* be a subset of S it is formally necessary to bind all

new terms introduced in step one in the definition of S* by existential quantifiers. This version

may easily be liberalized by introducing a new class of potential models M * such that members

of M * contain those from M as substructures. In the following, informal sketch of a theory net we implicitly use this more liberal version.

17) See (Littre, 1962), Vol. 6, Ch. VII, p. 374, or (Hippocrates, 1923), Vol. 2, (repr. 1959, transl. by Jones), Ch. X, pp. 161-3.

18) Prognostic, (Littre, 1962), Vol. 2, Chap. XX, p. 168.

19) (Littre, 1962), Vol. 2, p. 146 and (Hippocrates, 1923), Vol. 2, (repr. 1959, transl. by Jones), Ch. XIV, p. 29.

20) (Littre, 1962), Vol. 2, p. 148 and (Hippocrates, 1923), Vol. 2, (repr. 1959, transl. by Jones), Ch. XV, p. 31.

21) See (Balzer, 1985a).

22) See (Balzer, 1985) for the general, and (Balzer, et al., 1987), Chap. 2, for the more restricted

definition.

23) (Hippocrates, 1923), Vol. 1, (repr. 1957, transl. by Jones), Epidemics I, case VII, pp. 199-201.

24) (Hippocrates, 1923), Vol. 1, (repr. 1957, transl. by Jones), Epidemics I, case I, p. 187.

25) Compare (Balzer, et al., 1987), Chap. 2 for details.

26) See (Balzer, et al., 1987), Chap. 7 for a general account of approximation.

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Documents

A Reconstruction of the Hippocratic Humoral Theory of Health.W.balzer-A.eleftheriadis